Fagnano Orbits of Polygonal Dual Billiards

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.

Original languageEnglish (US)
Pages (from-to)279-286
Number of pages8
JournalGeometriae Dedicata
Volume77
Issue number3
DOIs
StatePublished - Jan 1 1999

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n-gon
Billiards
Orbit
Regular polygon
Periodic Orbits
Polygon

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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title = "Fagnano Orbits of Polygonal Dual Billiards",
abstract = "Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.",
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Fagnano Orbits of Polygonal Dual Billiards. / Tabachnikov, Sergei.

In: Geometriae Dedicata, Vol. 77, No. 3, 01.01.1999, p. 279-286.

Research output: Contribution to journalArticle

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